Question: Simplify to lowest terms. $\dfrac{24}{84}$
Explanation: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 24 and 84? $24 = 2\cdot2\cdot2\cdot3$ $84 = 2\cdot2\cdot3\cdot7$ $\mbox{GCD}(24, 84) = 2\cdot2\cdot3 = 12$ $\dfrac{24}{84} = \dfrac{2 \cdot 12}{ 7\cdot 12}$ $\hphantom{\dfrac{24}{84}} = \dfrac{2}{7} \cdot \dfrac{12}{12}$ $\hphantom{\dfrac{24}{84}} = \dfrac{2}{7} \cdot 1$ $\hphantom{\dfrac{24}{84}} = \dfrac{2}{7}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{24}{84}= \dfrac{2\cdot12}{2\cdot42}= \dfrac{2\cdot 2\cdot6}{2\cdot 2\cdot21}= \dfrac{2\cdot 2\cdot 3\cdot2}{2\cdot 2\cdot 3\cdot7}= \dfrac{2}{7}$